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QuizMultiple Choice

Solving Linear-Quadratic Systems

Question 1 • Algebra III A

The first step in determining the solution to the system of equations, y = –x2 – 4x – 3 and y = 2x + 5, algebraically is to set the two equations equal as –x2 – 4x – 3 = 2x + 5. What is the next step?

Answer
A
Set y = 0 in y = –x2 – 4x – 3.
B
Factor each side of the equation.
C
Use substitution to create a one-variable equation.
D
Combine like terms onto one side of the equation.

Explanation

After setting the equations equal, move all terms to one side so the equation is in the form 0 = ... . Subtract 2x and 5 from both sides: −x² − 4x − 3 = 2x + 5 becomes −x² − 6x − 8 = 0. This is combining like terms onto one side, so the correct choice is “Combine like terms onto one side of the equation.”

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